1. Symmetry

2. How do we define symmetry An object invariant under a transformation –Rotation –Translation –Time Lapse –Reflection How many symmetries does a cube have? 48

3. Curie’s Principle If certain causes produce certain effects, then the symmetries of the causes reappear in the effects produces If certain effects reveal a certain asymmetry, then this asymmetry will be reflected in the causes that give rise to them

4. An airplane An airplane has bilateral symmetry Does half a plane against a wall reproduce the flow past the airplane?

5. Bifurcation Symmetry “breaks” by creating an assortment of anti-symmetric states which sum to a symmetric state

6. Airplane Flying Has 2 steady states just off direct Switches between the two due to turbulence or other “imperfections” The overall “math” is symmetric, though there are anti-symmetric solutions

7. Symmetry in Biology

8. Gastrulation Start as spherically symmetric egg Lose symmetry with division Regain symmetry with blastula Lose symmetry as a sphere with a dimple

9. Breaking of Symmetry Causes –Difference of Pressure creates inward pressure –Cell-Cell movement Location selection –Breaking due to pressure will occur where walls are weaker –Cell-Cell movement could be caused by selectively changing cell-cell adhesion

10. What actually happens? Cells change their adhesion properties and move via “random” motion Axis is selected via signaling molecules established at the time of fertilization

11. Conclusions Small perturbations away from symmetry can cause substantial effects Biology often just “pushes” an organism in the correct direction